Amp Up for NEIEP Electrical Theory Thrills 2026 – Spark Your Success with Practice Exam 430!

In an AC circuit with sinusoidal voltage and current, instantaneous power is found by multiplying the instantaneous voltage by the instantaneous current: p(t) = v(t) · i(t). When the voltage and current are sinusoidal but may have a phase difference φ, the product p(t) contains both a constant part and a part that varies at twice the line frequency. If we write v(t) = V_m sin(ωt) and i(t) = I_m sin(ωt + φ), then p(t) = V_m I_m sin(ωt) sin(ωt + φ) can be rearranged to (V_m I_m / 2)[cosφ − cos(2ωt + φ)]. The cosφ term is constant, and the cos(2ωt + φ) term oscillates with time and averages to zero over one full cycle.

Thus the average power over a cycle comes from the constant part and equals (V_m I_m / 2) cosφ. When you translate to RMS values, this becomes P = V_rms I_rms cosφ. This cosφ factor is what we call the power factor: it tells you how much of the input power is actually being delivered as real power, with the remainder representing reactive power that shuttles back and forth without doing net work over a cycle.

So the best description is that the instantaneous power changes with time, while the average power over a cycle is given by VI cosφ for sinusoidal signals. If the circuit is purely resistive (φ = 0), the average power equals VI and p(t) still varies with time as v(t) i(t) for each moment, since voltage and current themselves vary. If there’s phase difference (reactive components), the average power drops below VI by the factor cosφ.